[r-t] What's the meaning of a method having aparticularfalsecourse head

Don Morrison dfm at mv.com
Mon Apr 25 20:29:03 UTC 2005

On Apr 25, 2005, at 6:00 AM, Richard Smith wrote:

> Here's my definition:
>   Let M be the set of a rows in the plain course of a
>   method, and let rM denote the set of rows in the course
>   with course head row, r:
>     rM = { ra : a in M }.
>   Define the set, F, of false course heads of M to be:
>     F = { f : fM intersection M != {} }.

Ah, that helps a lot. I think I'm 90% of the way towards being 
convinced your interpretation of A falseness is superior.

Also, Andrew Tibbetts made a joke about backstroke 87s that reminded me 
that A falseness really contains two different rows, not just one: 
12345678 and 13254768. This does make the "every method has A 
falseness" interpretation seem to have a little more meat to it, as 
well. And making it all the more interesting, perhaps, is that if you 
have non-plain bob lead heads isomorphic to the plain bob ones, but 
with something other than 12 or 18 as the lead end change, the image of 
that second FCH in A will be something different.

On Apr 25, 2005, at 6:00 AM, Richard Smith wrote:

> They don't form a group, but the set of all combinations of
> falseness "groups" form a monoid -- a mathematical structure
> similar to a group, but without the requirement for elements
> to have inverses.  The A falseness "group" forms the
> identity.  (This isn't a particularly insightful statement,
> but it does justify using the term "identity" to describe A
> falseness.)

I'm confused by this. I wasn't so much worried about inverses as 
closure. What's the monoid operation you're assuming? I don't think the 
usual cross product works, does it? For a random example, consider FCH 
group T, which contains, among others, FCHs 24536 and 43526. Permuting 
24536 by 24536 results in 25346, which is in T. But permuting 43526 by 
24536 results in 45236, which is in F. So the cross product T x T can't 
be any one of the FCH groups, can it? Is there some other operation of 
one FCH group on another you are considering that is closed?

Don Morrison <dfm at mv.com>
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anywhere on God's earth, and one's first impulse, standing
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